Question: Simplify the following expression: $\dfrac{18p}{14p^5}$ You can assume $p \neq 0$.
Solution: $ \dfrac{18p}{14p^5} = \dfrac{18}{14} \cdot \dfrac{p}{p^5} $ To simplify $\frac{18}{14}$ , find the greatest common factor (GCD) of $18$ and $14$ $18 = 2 \cdot 3 \cdot 3$ $14 = 2 \cdot 7$ $ \mbox{GCD}(18, 14) = 2 $ $ \dfrac{18}{14} \cdot \dfrac{p}{p^5} = \dfrac{2 \cdot 9}{2 \cdot 7} \cdot \dfrac{p}{p^5} $ $\phantom{ \dfrac{18}{14} \cdot \dfrac{1}{5}} = \dfrac{9}{7} \cdot \dfrac{p}{p^5} $ $ \dfrac{p}{p^5} = \dfrac{p}{p \cdot p \cdot p \cdot p \cdot p} = \dfrac{1}{p^4} $ $ \dfrac{9}{7} \cdot \dfrac{1}{p^4} = \dfrac{9}{7p^4} $